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Q-fuzzy structure on JU-algebra.

Selamawit Hunie Gelaw1, Birhanu Assaye Alaba1, Mihret Alamneh Taye1

  • 1Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, 79, Ethiopia.

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|March 27, 2025
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Summary
This summary is machine-generated.

This study introduces Q-fuzzy sets to JU-algebras, defining Q-fuzzy JU-subalgebras and JU-ideals. It explores their properties and introduces Doubt and Normal fuzzy structures for handling uncertainty in algebra.

Keywords:
Doubt Q-Fuzzy JU-algebraJU-algebraLevel subsetsNormal Q-Fuzzy JU-algebraQ-Fuzzy JU- IdealQ-Fuzzy JU-subalgebra

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Area of Science:

  • Abstract Algebra
  • Fuzzy Set Theory
  • Mathematical Structures

Background:

  • JU-algebras are a key area within abstract algebra.
  • Fuzzy set theory is employed to address uncertainty in algebraic systems.
  • This research applies Q-fuzzy set concepts to JU-algebras.

Purpose of the Study:

  • To define and investigate Q-fuzzy JU-subalgebras and Q-fuzzy JU-ideals.
  • To analyze the properties of lower and upper level subsets of these fuzzy structures.
  • To introduce and explore Doubt and Normal Q-fuzzy JU-subalgebras and JU-ideals.

Main Methods:

  • Definition of Q-fuzzy JU-subalgebras and Q-fuzzy JU-ideals within JU-algebras.
  • Analysis of lower and upper level subsets of the defined fuzzy structures.
  • Introduction of Doubt and Normal fuzzy concepts for JU-algebraic structures.

Main Results:

  • Novel definitions for Q-fuzzy JU-subalgebras and Q-fuzzy JU-ideals are established.
  • Key properties, including level subsets, of these fuzzy structures are examined.
  • Doubt and Normal fuzzy structures are introduced, offering nuanced ways to represent uncertainty.

Conclusions:

  • The study successfully extends JU-algebra theory with new fuzzy structures.
  • It provides a framework for analyzing uncertainty in algebraic contexts.
  • The introduced concepts pave the way for future research in fuzzy algebra and its applications.